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Answer:
19.3°
Step-by-step explanation:
Isabella is making a flag that is 20 meters wide and 7 meters high. We need to find the angle of elevation of the diagonal from the bottom-left corner to the right side of the flag. To do this, we can use the tangent trigonometry operation.
Solving:
[tex]\subsection*{The Triangle:}\begin{itemize} \item The base (horizontal distance) is \( d = 20 \) meters. \item The height (vertical distance) is \( h = 7 \) meters.\end{itemize}[/tex]
[tex]\subsection*{Tangent Function:}The tangent of the angle of elevation \( \theta \) is given by the ratio of the opposite side (height) to the adjacent side (base):\[\tan(\theta) = \frac{h}{d} = \frac{7}{20}\][/tex]
[tex]\subsection*{Find the Angle:}To find the angle \( \theta \), we use the arctangent(inverse tangent) function:\[\theta = \tan^{-1}\left(\frac{7}{20}\right)\][/tex]
[tex]\subsection*{Use a Calculator:}\[\theta \approx \tan^{-1}(0.35) \approx \boxed{19.3^\circ}\][/tex]
Therefore, the angle of elevation of the diagonal is 19.3 degrees.